Winglet system and method

ABSTRACT

A winglet system for an aircraft wing may include an upper winglet and a lower winglet mounted to a wing tip. The lower winglet may have a static position when the wing is subject to an on-ground static loading. The lower winglet may be configured such that upward deflection of the wing under an approximate 1-g flight loading causes the lower winglet to move upwardly and outwardly from the static position to an in-flight position resulting in an effective span increase of the wing under the approximate 1-g flight loading relative to the span of the wing under the on-ground static loading. The lower winglet may have a length of approximately 50-80 percent of a length of the upper winglet.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is a continuation application of and claimspriority to pending U.S. application Ser. No. 13/436,355 filed on Mar.30, 2012 and entitled PERFORMANCE-ENHANCING WINGLET SYSTEM AND METHOD,the entire contents of which is expressly incorporated by referenceherein.

FIELD

The present disclosure relates generally to aerodynamics and, moreparticularly, to wing tip devices such as for the wings of an aircraft.

BACKGROUND

Induced drag is generated by an aircraft wing due to the redirection ofair during the generation of lift as the wing moves through the air. Theredirection of the air may include spanwise flow along the underside ofthe wing along a generally outboard direction toward the wing tips wherethe air then flows upwardly over the wing tips. The air flowing over thetips joins a chordwise flow of air over the wing resulting in theformation of wing tip vortices. The wing tip vortices are fed by othervortices that are shed by the trailing edge of the wing. The downwash ofvortices trailing from the wing reduces the effective angle of attack ofthe wing which results in a reduction in generated lift.

Winglets provide a means for reducing the negative effects of induceddrag such as by effectively increasing the length of the trailing edgeof the wing. The effective increase in the length of the trailing edgemay spread out the distribution of the vortices which may reduce lossesfrom induced drag. In this regard, winglets may provide a significantreduction in induced drag which may improve the performance of theaircraft. Furthermore, winglets may provide an increase in effectivetrailing edge length without increasing the length of the wing leadingedge. Additionally, by adding winglets to the wings instead ofincreasing the wing span in the conventional manner by extending thewing tips, the added weight, cost, and complexity associated withlengthening of leading edge lift-enhancement devices (e.g., slats,Krueger flaps) may be avoided.

However, conventional winglets may increase the aerodynamic loading atthe wing tips which may result in an increase in wing bending under highlift conditions. The increase in wing bending may require strengtheningor stiffening of the wing structure which adds weight and which maynegate the drag-reducing benefits provided by the winglets. In addition,the center of gravity of conventional winglets may be located at arelatively long distance from the torsional axis of the wing which mayaffect the flutter characteristics of the wing. In an attempt tocounteract the inertial effects of conventional winglets, ballast may beadded to the leading edge of the wing tip. Unfortunately, the additionof ballast may negate some of the drag-reducing benefits provided by thewinglet. Conventional winglets may also suffer reduced aerodynamicefficiency due to flow separation that may occur at high loadingconditions including at low speeds.

As can be seen, there exists a need in the art for a wing tip devicethat may reduce the induced drag of a wing without increasing wingbending. In addition, there exists a need in the art for a wing tipdevice which minimizes the impact on flutter characteristics of thewing. Furthermore, there exists a need in the art for a wing tip devicethat does not require the addition of ballast to overcome the inertialeffects of a winglet on the flutter characteristics of the wing.

SUMMARY

Any one or more of the above-noted needs associated with conventionalwinglets may be specifically addressed and alleviated by the presentdisclosure which provides a winglet system for an aircraft wing whereinthe winglet system includes an upper winglet and a lower winglet mountedto a wing tip. The lower winglet may have a static position when thewing is subjected to a ground static loading. The lower winglet may beconfigured such that upward deflection of the wing under an approximate1-g flight loading causes the lower winglet to move from the staticposition to an in-flight position and resulting in a relative spanincrease of the wing.

Also disclosed is an aircraft having a pair of wings with each winghaving a wing tip. The aircraft may include an upper winglet and a lowerwinglet mounted to each one of the wing tips. The lower winglets may besized and oriented such that upward deflection of the wings under anapproximate 1-g flight loading results in a relative span increase ofthe wings.

In a further embodiment, disclosed is a method of enhancing theperformance of an aircraft including the step of providing an upperwinglet and a lower winglet on a wing. The lower winglet may have astatic position when the wing is subject to a ground static loading. Themethod may further include upwardly deflecting the wing under anapproximate 1-g flight loading. In addition, the method may includemoving the lower winglet from the static position to an in-flightposition during upward deflection of the wing. The method may alsoinclude causing a relative span increase of the wing when moving thelower winglet from the static position to the in-flight position.

The features, functions and advantages that have been discussed can beachieved independently in various embodiments of the present disclosureor may be combined in yet other embodiments, further details of whichcan be seen with reference to the following description and drawingsbelow.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other features of the present disclosure will become moreapparent upon reference to the drawings wherein like numbers refer tolike parts throughout and wherein:

FIG. 1 is a perspective illustration of an aircraft having a wingletsystem mounted on each wing tip of the wings;

FIG. 2 is a front view of the aircraft illustrating an upper winglet anda lower winglet included with the winglet system mounted to each wingtip;

FIG. 3 is a side view of one of the winglet systems taken along line 3of FIG. 2 and illustrating the upper winglet and the lower wingletmounted to a wing tip;

FIG. 4 is a top view of the upper winglet taken along line 4 of FIG. 3and illustrating a twist angle or washout that may optionally beincorporated into the upper winglet;

FIG. 5 is a top view of the lower winglet taken along line the 5 of FIG.3 and illustrating a twist angle that may optionally be incorporatedinto the lower winglet;

FIG. 6 is a schematic front view of one of the wings in a jigged shape,in a downwardly-deflected ground static loading shape, and in anupwardly-deflected 1-g flight loading (e.g., 1-g wing loading) shape;

FIG. 7 is a schematic view of the relative positions of the upper andlower winglets for the wing in the three different shapes illustrated inFIG. 6;

FIG. 8 is a front view of the aircraft illustrating the lower winglet oneach wing tip being moved from a static position, wherein the wing issubjected to a ground static loading, to an in-flight position, whereinthe wing is subjected to the approximate 1-g flight loading, and furtherillustrating an increase in effective wing span occurring in response tomovement of the lower winglets from the static position to the in-flightposition;

FIG. 9 is a side view of an embodiment of a single upper winglet havinga center of gravity located at a longitudinal offset from a torsionalaxis of the wing;

FIG. 10 is a side view of the winglet system disclosed herein whereinthe combination of the upper and lower winglet results in a combinedcenter of gravity located at a reduced longitudinal offset to thetorsional axis relative to the greater longitudinal offset for thesingle upper winglet and which advantageously minimizes the inertialeffects of the winglet system on the flutter of the wing;

FIG. 11 is a side view of an alternative embodiment of the wingletsystem wherein the trailing edges of the upper winglet and lower wingletare generally aligned with the wing trailing edge;

FIG. 12 is a side view of a further embodiment of the winglet systemhaving leading edge root gloves mounted at a juncture of the wing tip toeach of the upper winglet and the lower winglet;

FIG. 13 is a perspective view of an embodiment of the winglet systemillustrating a center of pressure of the lower winglet located aft ofthe wing torsional axis due to a relatively large sweep angle of thelower winglet and due to a relatively small anhedral angle of the lowerwinglet;

FIG. 14 is a side view of the winglet system taken along line 14 of FIG.13 and illustrating a nose-down moment exerted on the wing tip inresponse to an increase in lift of the lower winglet in response to agust load; and

FIG. 15 is a flow diagram having one or more operations that may beincluded in a method of operating an aircraft.

DETAILED DESCRIPTION

Referring now to the drawings wherein the showings are for purposes ofillustrating various embodiments of the present disclosure, shown inFIG. 1 is a perspective view of an aircraft 10 having a fuselage 12. Thefuselage 12 may include a cabin for passengers and flight crew. Thefuselage 12 may extend from a nose at a forward end 24 of the aircraft10 to an empennage 18 at an aft end 26 of the fuselage 12. The empennage18 may include one or more tail surfaces such as a vertical stabilizer22 and/or a horizontal stabilizer 20 for control of the aircraft 10. Theaircraft 10 may further include a pair of wings 50, one or morepropulsion units 16, and nose and main landing gear 14 (FIG. 2). Thewings 50 may include one or more winglet systems 98 as disclosed herein.Each winglet system 98 may comprise an upper winglet 100 and a lowerwinglet 200 and which may be mounted to a wing tip 56 of a wing 50.

It should be noted that although the winglet system 98 of the presentdisclosure is described in the context of a fixed wing passengeraircraft 10 such as the tube-and-wing aircraft 10 illustrated in FIG. 1,any one of the various winglet system 98 embodiments may be applied toany aircraft of any configuration, without limitation. For example, thewinglet system 98 may be applied to any civil, commercial, or militaryaircraft. In addition, the embodiments of the winglet system 98disclosed herein may be applied to alternative aircraft configurationsand are not limited to the tube-and-wing aircraft 10 configurationillustrated in FIG. 1. For example, the disclosed embodiments may beapplied to hybrid wing-body aircraft or blended-wing aircraft.

The winglet system 98 may also be applied to aerodynamic surfaces orlifting surfaces other than wings 50. For example, the winglet system 98may be applied to a canard, to a control surface such as a horizontalstabilizer, or to any other lifting surface where it is desired tomitigate the adverse effects of induced drag and/or to enhanceaerodynamic performance. Advantageously, the upper and lower winglets100, 200 as disclosed herein may be provided in relatively large sizeswith relatively long root chords and relatively high degrees of sweepand/or taper. The lower winglet 200 is advantageously provided with arelatively limited amount of anhedral angle 224 (FIG. 8) which resultsin an increase in effective wing span 80 (FIG. 8) when the wings 50 areaeroelastically deflected upwardly such as under an approximate 1-gflight loading 78 (FIG. 6) during cruise flight. In addition, the lowerwinglet 200 may also be configured to aeroelastically deflect upwardlyunder the approximate 1-g flight loading 78 and which may result in arelative span increase 84 (FIG. 7) and may contribute toward increasingthe effective wing span 80 (FIG. 7) of the wings 50 as illustrated inFIGS. 6-8 and described in greater detail below. Advantageously, byincreasing the effective wing span 80 due to the upward deflection ofthe wing 50 and/or due to upward deflection of the lower winglet 200,the lift-to-drag performance of the aircraft 10 may be improved.

In FIG. 1, the installation of the winglet system 98 on the aircraft 10may be defined with regard to a coordinate system having a longitudinalaxis 28, a lateral axis 30, and a vertical axis 32. The longitudinalaxis 28 may be defined as extending through a general center of thefuselage 12 between the forward end 24 and the aft end 26. The lateralaxis 30 may be oriented orthogonally relative to the longitudinal axis28 and may extend generally along the wing 50 outboard directionsrelative to a center of the fuselage 12. The vertical axis 32 may beoriented orthogonally relative to the longitudinal and lateral axes 28,30. Each one of the wings 50 of the aircraft 10 shown in FIG. 1 mayextend from a wing root 52 having a root chord 54 to a wing tip 56having a tip chord 58. Each wing 50 may have upper and lower surfaces64, 66 and may include a wing leading edge 60 and a wing trailing edge62. In the embodiment shown, the wing leading edge 60 may be formed at awing sweep angle 68. Each wing 50 may extend upwardly at a dihedralangle 70. However, the wings 50 upon which the winglet systems 98 may bemounted may be provided in any geometric configuration and are notlimited to the above-described arrangement for the aircraft 10 shown inFIG. 1.

FIG. 2 is a front view of the aircraft 10 supported by the landing gear14 and illustrating a winglet system 98 mounted to the wing tip 56 ofeach wing. The wings 50 are shown in a jigged shape 74 (FIG. 6) whereinthe wings 50 are relatively straight as may occur when the wings 50 areconstrained by assembly tooling during the manufacturing of the aircraft10. In one example, a jigged shaped (e.g., jigged shape 74—FIG. 6) maybe defined as an equilibrium state (e.g., an unloaded state) of anelastic member (e.g., a wing 50). As indicated in greater detail below,when the aircraft 10 is supported by the landing gear 14, the wings 50may typically assume a slightly downwardly-deflected shape under aground static loading 76 (FIG. 6) due to the gravitational force actingon the mass of the wings 50, the propulsion units 16, and/or othersystems supported by the wings 50.

Each wing tip 56 may include a winglet system 98 comprising the upperwinglet 100 and the lower winglet 200. The upper winglet 100 may have anupper winglet root 102 which may be affixed or otherwise coupled to thewing 50 at the wing tip 56. The upper winglet 100 may extend as arelatively straight member toward the upper winglet tip 106. Likewise,the lower winglet 200 may have a lower winglet root 202 which may beaffixed to the wing 50 at the wing tip 56. In an embodiment, the lowerwinglet root 202 may intersect or may be joined with the upper wingletroot 102 at the wing tip 56. The lower winglet 200 may extend as arelatively straight member toward the lower winglet 206 tip. However,the upper winglet 100 and/or the lower winglet 200 may be provided in anon-straight shape and may include curved shapes or contoured shapes andmay further include combinations of straight shapes, curved shapes, andcontoured shapes.

The upper winglet 100 may have an upper winglet length 118 (e.g., asemi-span) extending from the upper winglet root 102 to the upperwinglet tip 106. In the embodiment shown, the upper winglet length 118may be longer than a lower winglet length 218 of the lower winglet 200.In an embodiment, the lower winglet 200 may have a lower winglet length218 of at least approximately 50 percent of the upper winglet length 118of the upper winglet 100. In a further embodiment, the lower winglet 200may have a lower winglet length 218 in the range of from approximately50 to 80 percent of the upper winglet length 118 of the upper winglet100. In an embodiment of a commercial transport aircraft 10, the upperwinglet 100 may be provided in an upper winglet length 118 of fromapproximately 50 to 150 inches. For example, the upper winglet 100 maybe provided in an upper winglet length 118 of from 90 to 110 inches. Thelower winglet length 218 may extend from the lower winglet root 202 tothe lower winglet tip 206 and may be provided in a lower winglet length218 of from approximately 30 to 100 inches. For example, the lowerwinglet 200 may be provided in a lower winglet length 218 of from 50 to70 inches. However, the upper winglet 100 and the lower winglet 200 maybe provided in any length and are not limited to the length rangesmentioned above. Furthermore, although not shown, the winglet system 98may be provided in an embodiment wherein the lower winglet 200 is longerthan the upper winglet 100. In addition, in one or more of embodiments,the lower winglet 100 may be configured such that the lower winglet tip206 is located approximately at the intersection of the gate span limit38 (FIG. 6) and the roll and pitch clearance line 42 (FIG. 6) asdescribed below.

In FIG. 3, shown is a side view of the winglet system 98 mounted to thewing tip 56 of the wing 50. The upper winglet root 102 is joined to thewing tip 56 at a wing-upper winglet juncture 150. Likewise, the lowerwinglet root 202 is joined to the wing tip 56 at a wing-lower wingletjuncture 152. Although the illustration shows the upper winglet root 102and lower winglet root 202 being respectively mounted to the upper andlower portions of a wing tip 56, the winglet system 98 may be configuredsuch that the upper winglet 100 at least partially intersects the lowerwinglet 200 at an upper winglet-lower winglet juncture 154. In thisregard, the upper winglet root 102 and the lower winglet root 202 may bemounted to the wing tip 56 at any vertical location relative to oneanother. In addition, although the figures of the present disclosureshow the upper winglet root 102 and the lower winglet root 202 as beinggenerally aligned with one another at the juncture of the upper andlower winglet roots 102, 202 with the wing tip 56, the upper wingletroot 102 may be joined to the wing tip 56 such that the upper wingletroot 102 is located forward of the lower winglet root 202.Alternatively, the lower winglet root 202 may be joined to the wing tip56 such that the lower winglet root 202 is located forward of the upperwinglet root 102. In this regard, the upper winglet root 102 may bejoined to the wing tip 56 such that the upper winglet leading edge 112is located forward of the lower winglet leading edge 212, or vice versa.Likewise, the upper winglet root 102 may be joined to the wing tip suchthat the upper winglet trailing edge 112 is located forward of the lowerwinglet trailing edge 212, or vice versa.

Furthermore, although the present disclosure illustrates the upperwinglet root 102 and the lower winglet root 202 as being generallyaligned with one another in a lateral direction (e.g., along a directionparallel to the lateral axis 30—FIG. 2), the upper winglet root 102(FIG. 3) and the lower winglet root 202 (FIG. 3) may be joined to thewing tip 56 such that the upper winglet root 102 is located furtheroutboard (e.g., further away from the wing root 52—FIG. 1) than thelower winglet root 202. Alternatively, the lower winglet root 202 may belocated further outboard than the upper winglet root 202. In thisregard, the wing tip 56 may be defined as approximately the outermostten (10) percent of the length of the wing 50 from the wing root 52(FIG. 1) to the wing tip 56 (FIG. 1). The upper winglet root 102 and thelower winglet root 202 are not limited to being joined to the wing 50 atthe extreme outermost end of the wing tip 56. For example, the upperwinglet root 102 and the lower winglet root 202 of the upper and lowerwinglets 100, 200 may be joined to the wing(s) 50 at any location suchthat the lower winglets 200 (FIG. 8) on the oppositely-disposed wingtips 56 (FIG. 8) of the aircraft 10 (FIG. 8) define the effective wingspan 82 (FIG. 8) when the wings 50 are under the approximate 1-g flightloading 78 (FIG. 8). In an embodiment, the upper winglet root 102 and/orthe lower winglet root 202 may be joined to the wing 50 at any locationfrom the extreme outermost end of the wing tip 56 to any location on theoutermost ten (10) percent of the length of the wing 50.

In FIG. 3, the upper winglet 100 and the lower winglet 200 may be sweptaftwardly and may additionally be formed with a taper ratio of tip chord108, 208 to corresponding root chord 104, 204. In an embodiment, thetaper ratio of the upper winglet 100 and/or the lower winglet 200 may bein the range of from approximately 0.15 to 0.50. For example, the taperratio of the upper winglet 100 and/or the lower winglet 200 may be inthe range of from approximately 0.20 to 0.25. However, the upper winglet100 and/or the lower winglet 200 may be formed with a taper ratio thatis outside of the 0.15 to 0.50 range and may be selected in conjunctionwith a twist angle 122 or washout that may optionally be included in theupper winglet 100 and/or the lower winglet 200 as described below toprovide a desired load distribution.

The upper winglet 100 and the lower winglet 200 each have a leading edge110, 210 and a trailing edge 112, 212. In an embodiment, theintersection of the upper winglet leading edge 110 and/or the lowerwinglet leading edge 210 with the wing tip 56 may be located aft of thewing leading edge 60 at the wing tip 56 which may minimize flowseparation at certain flight conditions. In the embodiment shown in FIG.3, the upper and lower winglet 100, 200 are configured such that theupper winglet leading edge 110 intersects the lower winglet leading edge210 at a location that is aft of the wing leading edge 60. It iscontemplated that the intersection of the upper winglet leading edge 110and/or the lower winglet leading edge 210 with the wing tip 56 may begenerally coincident with or located approximately at the wing leadingedge 60. The upper winglet trailing edge 112 and/or the lower winglettrailing edge 212 may join or intersect the wing tip 56 at a locationthat is forward of the wing trailing edge 62 as shown in the embodimentof FIG. 3. However, the upper winglet trailing edge 112 and/or the lowerwinglet trailing edge 212 may join or intersect the wing tip 56 at anylocation that is no further aft than the wing trailing edge 62.

Even further, the winglet system 98 may be provided in alternativeembodiments wherein the upper winglet trailing edge 112 and/or the lowerwinglet trailing edge 212 may intersect the wing tip 56 at a locationthat is approximately coincident with the wing trailing edge 62 or at alocation that is generally aft of the wing trailing edge 62 as describedbelow. In any embodiment disclosed herein, the winglet system 98 may beconfigured such that the upper winglet root chord 104 and/or the lowerwinglet root chord 204 may be longer than the wing tip chord 58. Inaddition, the winglet system 98 may be configured such that the upperwinglet root chord 104 and/or the lower winglet root chord 204 may beshorter than the wing tip chord 58. In an embodiment, the winglet system98 may be configured such that a portion of the upper winglet root chord104 and/or lower winglet root chord 204 extends forward of the wingleading edge 60. Similarly, the winglet system may be configured suchthat a portion of the upper winglet root chord 104 and/or lower wingletroot chord 204 extends aft of the wing trailing edge 62.

In FIG. 3, the upper winglet 100 and the lower winglet 200 each have aroot chord 104, 204 at the location where the upper winglet 100 andlower winglet 200 respectively join the wing tip 56. The wing tip 56 hasa wing tip chord 58. The winglet system 98 may be configured such thatthe upper winglet root chord 104 has a length that is at leastapproximately 50 percent of the length of the wing tip chord 58.Likewise, the lower winglet 200 may be configured such that the lowerwinglet root 202 chord has a length that is at least approximately 50percent of the length of the wing tip chord 58. In an embodiment, theupper winglet root chord 104 and/or the lower winglet root chord 204 mayeach have a length in the range of from approximately 60 to 100 or morepercent of the length of the wing tip chord 58. Additional parasiticdrag that may result from a relatively long root chord of the upperwinglet 100 and/or the lower winglet 200 may be mitigated by including aleading edge root glove 138, 238 (FIG. 12) at a juncture 150 of theupper winglet 100 to the wing tip 56 and/or at a juncture 152 of thelower winglet 200 to the wing tip 56.

The leading edge root gloves 138, 238 may minimize the additionalparasitic drag generated by the relatively long upper and lower wingletroot chords 104, 204 at the juncture thereof with the wing tip 56 asdescribed below by avoiding the need to carry the length of the upperand lower winglet root chords 104, 204 all the way to the respectiveupper and lower winglet tip 106, 206. Advantageously, by sizing theupper winglet 100 and/or lower winglet 200 such that the upper wingletroot chord 104 and/or the lower winglet root chord 204 have a length ofat least approximately 50 percent of the length of the wing tip chord58, the aerodynamic load of the wing tip 56 may be divided between theupper winglet 100 and the lower winglet 200 as opposed to an arrangementwherein a single upper winglet 280 (FIG. 9) is provided for carrying thefull aerodynamic load of the wing tip 56.

In an example of the embodiment of FIG. 3, for a wing tip 56 having asection lift coefficient of 1.0 and wherein the upper winglet root chord104 and the lower winglet root chord 204 are substantially equal inlength to the length of the wing tip chord 58, the upper winglet root102 carries a section lift coefficient of 0.5 and the lower winglet root202 carries a section lift coefficient of 0.5. In contrast, in anarrangement wherein a single upper winglet 280 (FIG. 9) is provided withno lower winglet, the single upper winglet 280 would carry the fullsection lift coefficient of 1.0. A higher section lift coefficient atthe root of the single upper winglet 280 may correspond to a greaterpropensity for flow separation as may occur in cruise flight and/or athigh-lift conditions. Such flow separation may result in reducedeffectiveness of the single upper winglet 280 and may lead to buffetingor other undesirable characteristics. A further advantage of thecombination of upper and lower winglets 100, 200 of the presentdisclosure instead of a single upper winglet 280 is that a single upperwinglet 280 may not provide an effective increase in wing span because asingle upper winglet tip would move inwardly (e.g., toward an opposingupper winglet tip mounted on an opposite wing of the aircraft) as thewings are deflected upwardly under a 1-g wing loading.

FIG. 4 is a top view of the upper winglet 100 mounted to the wing tip56. The upper winglet leading edge 110 may be oriented at a leading edgesweep angle 114 of between approximately 20 and 70 degrees. The sweepangles 114, 214 in FIGS. 4-5 may be measured relative to the lateralaxis 30 (FIG. 1) of the aircraft 10 (FIG. 1). The upper winglet leadingedge 110 may optionally be provided with a leading edge sweep angle 114that is outside of the 20-70 degree range. FIG. 4 further illustrates anupper winglet twist angle 122 or washout that may optionally beincorporated into the upper winglet 100. Twist angle 122 may beincorporated into the upper winglet 100 as a means to control the loaddistribution along the upper winglet 100. In FIG. 4, the upper winglettwist angle 122 at any point along the upper winglet 100 may be definedrelative to a root chord lower surface reference line 105 whichrepresents the angle of incidence of the lower surface of the upperwinglet root 102. In an embodiment, the upper winglet 100 may beprovided with an upper winglet twist angle 122 of up to approximately −7degrees wherein the upper winglet tip 106 may be oriented at a greaternegative angle of incidence than the upper winglet root 102. Forexample, the upper winglet 100 may be provided with an upper winglettwist angle 122 of approximately −3 to −5 degrees. The upper winglettwist angle 122 along the upper winglet root 102 toward the upperwinglet tip 106 may have a constant rate along the upper winglet length118. However, the upper winglet twist angle 122 may be applied at avarying rate along the upper winglet length 118.

FIG. 5 is a top view of the lower winglet 200 mounted to the wing tip56. The lower winglet leading edge 210 may be oriented at a relativelylarge leading edge sweep angle 214 of between approximately 20 and 70degrees although the leading edge sweep angle 214 may be larger orsmaller than the 20-70 degree range. Advantageously, the relativelylarge leading edge sweep angle 214 of the lower winglet 200 provides araked arrangement for the lower winglet 200 which locates the center ofpressure 230 (FIG. 14) of the lower winglet 200 relatively far aft ofthe torsional axis 72 (FIG. 14) of the wing 50. As described in greaterdetail below, under certain flight conditions such as during a wind gust46 (FIG. 14), the location of the lower winglet 200 center of pressure230 at a point that is aft of the torsional axis 72 of the wing 50advantageously results in a nose-down moment 250 (FIG. 14) whicheffectively rotates the wing tip 56 in a nose-down direction about thetorsional axis 72 (FIG. 9) and temporarily reduces the effective angleof incidence 48 (FIG. 14) at the wing tip 56. The reduction in theeffective angle of incidence 48 at the wing tip 56 results in areduction in the bending load that would otherwise be imposed on thewing 50.

Furthermore, a relatively large leading edge sweep angle 214 of thelower winglet 200 combined with a relatively thick leading edge airfoil(not shown) of the lower winglet 200 may result in a well-defined,steady vortex (not shown) developing on the lower winglet 200 and whichmay reduce the propensity towards flow separation and buffeting atlow-speed, high-lift conditions. As indicated above with regard to theupper winglet 100, the lower winglet 200 may be provided with a twistangle 222. In FIG. 5, the lower winglet twist angle 222 at any pointalong the lower winglet 200 may be defined relative to a root chordlower surface reference line 205 which is a line representing the angleof incidence of the lower surface of the lower winglet root 202. Thelower winglet 200 may be provided with a twist angle 222 of up toapproximately −7 degrees such as a twist angle 222 of approximately −3to −4 degrees and which may provide a means to control the loaddistribution along the length of the lower winglet 200.

FIG. 6 is a schematic front view of the aircraft 10 showing a wing 50 inone of three different shapes representing constraints that may dictatethe size and orientation of the upper and lower winglets 100, 200. Theaircraft wing 50 is shown in solid lines in a jigged shape 74 which mayrepresent a theoretical shape of the wing 50 when constrained byassembly tooling such as during manufacturing of the aircraft 10 asdescribed above. The wing 50 is also shown in phantom lines in adownwardly-deflected ground static loading 76 shape which the wing 50may assume such as when the aircraft 10 is parked at a gate of anairport terminal. The ground static loading 76 shape of the wing 50 isin response to gravitational force acting on the mass of the wings 50,propulsion units 16 (FIG. 1), and/or other systems. The wing 50 is alsoshown in phantom lines in an upwardly-deflected 1-g flight loading 78shape (e.g., 1-g wing loading) as may occur when the aircraft 10 is inlevel cruise flight and subjected to aerodynamic lifting loads.

FIG. 6 illustrates the rigging or configuration of the winglet system 98on a typical aircraft 10 wherein the upper winglet 100 and the lowerwinglet 200 are located at the maximum outboard position subject toseveral constraints. For example, the aircraft 10 is supported on thestatic ground line 40 which may represent an airport ramp (not shown) onwhich the aircraft 10 may be parked at a gate near a terminal. Theaircraft 10 may be subject to a gate span limit 38 represented by thevertical phantom line in FIG. 6. The gate span limit 38 may be apredefined limit. For example, the gate span limit may be predefined bya regulatory agency as the maximum wing span of an aircraft that maysafely operate within or fit the geometric constraints of a gatelocation at an airport terminal. Gate span limits 38 may be categorizedinto groups or codes based on maximum wing span. In this regard, theFederal Aviation Administration (FAA) and the International CivilAviation Organization (ICAO) categorize aircraft as one of Group Ithrough Group VI (FAA), or as one of Code A through Code F (ICAO). Forexample, a Code C aircraft has a gate span limit of up to, but notincluding, 36 meters. In the context of the present disclosure, a Code Caircraft having winglet systems 98 as disclosed herein would be limitedto operating at airport gates wherein the effective wing span 80 (FIG.6) between the outermost points on the lower winglet tips 206 is lessthan 36 meters when the wings 50 are under ground static loading 76.

Also shown in FIG. 6 is a roll and pitch clearance line 42 which isillustrated as an angled line extending upwardly from the landing gear14 to provide clearance for the aircraft 10 wings 50 to avoid tip strikeof a wing tip 56 such as during takeoff and/or landing. The upperwinglet 100 and the lower winglets 200 are sized and oriented such thatthe neither the upper winglet 100 nor the lower winglet 200 violates(e.g., extends beyond) the gate span limit 38. The upper winglet 100 andthe lower winglet 200 may be configured such that the upper winglet tip106 and the lower winglet tip 206 terminate at approximately the samelateral location at the gate span limit 38 when the wing 50 is under anon-ground static loading 76. The lower winglet 200 is also sized andoriented to avoid violating the roll and pitch clearance line 42. In anembodiment, the lower winglet 200 may be sized and configured such thatthe lower winglet tip 206 is located approximately at the intersectionof the gate span limit 38 and the roll and pitch clearance line 42. FIG.6 further illustrates the upward deflection of the wing 50 under theapproximately 1-g flight loading 78 representing the wing shape duringcruise flight.

FIG. 7 illustrates an absolute span increase 86 that may be provided bythe lower winglet 200 as the wing 50 moves from the on-ground staticloading 76 shape to the approximately 1-g flight loading 78 shape. FIG.7 further illustrates the relative span increase 84 of the lower winglet200 relative to the upper winglet 100. In an embodiment, the lowerwinglet 200 may be configured such that upward deflection of the wing 50under the approximate 1-g flight loading 78 causes the lower winglet 200to move from the static position 240 to an in-flight position 242 andresulting in the relative span increase 84 of the wing 50. In anembodiment as shown in FIG. 7, the upper winglet tip 106 may besubstantially vertically aligned with the lower winglet tip 206 such asat the gate span limit 38 under on-ground static loading 76 of the wing50. The relative span increase 84 may be defined as the horizontaldistance between the upper winglet tip 106 and the lower winglet tip 206when the lower winglet 200 is in the in-flight position 242.

The winglet system 98 may also be provided in an embodiment wherein theupper winglet tip 106 is not vertically aligned (not shown) with thelower winglet tip 206 when the wing 50 is under on-ground static loading76 such that the relative span increase 84 is the difference between thehorizontal distance between the upper and lower winglet tip 106, 206when the lower winglet 200 is in the static position 240, and thehorizontal distance between the upper and lower winglet tip 106, 206when the lower winglet 200 is in the in-flight position 242.Advantageously, the orientation and sizing of the lower winglet 200 mayresult in an increase in effective wing span 80 during upward deflectionof the wing 50 under the approximate 1-g flight loading 78 relative tothe reduction in effective span that would occur with a single upperwinglet 280 (FIG. 9) mounted to each of the wing tips 56 (FIG. 8). Thewinglet system 98 as disclosed herein may also be configured such thatthe relative span increase 84 or the increase in effective wing span 80is due at least in part to aeroelastic bending or deflection of thelower winglet 200 and/or due to movement (e.g., pivoting) of the lowerwinglet 200 at the juncture of the lower winglet root with the wing tip56.

FIG. 8 is a front view of the aircraft 10 illustrating the lower winglet200 on each wing tip 56 moved from a static position 240, wherein thewing 50 is subjected to a ground static loading 76, to an in-flightposition 242, wherein the wing 50 is subjected to the approximate 1-gflight loading 78. The in-flight position 242 may be the result of anupward and outward movement of the lower winglet tip 206 from the staticposition 240 along the arc as shown in FIG. 6. Also shown in FIG. 8 isthe effective wing span 80 of the wings 50 in the ground static loading76 condition and the effective wing span 82 of the wings 50 in theapproximate 1-g flight loading 78. The increase in wing span occurs inresponse to movement of the lower winglets 200 from the static position240 to the in-flight position 242 along the arc illustrated in FIG. 6.The effective wing span 82 is measured between the outermost portions ofthe lower winglet tips 206 on opposing wing tips 56 of an aircraft 10.

In FIG. 8, the lower winglet 200 is also advantageously oriented at ananhedral angle 224 of no less than approximately 15 degrees duringupward deflection of the wing 50 under the approximate 1-g flightloading 78. In a further embodiment, the lower winglets 200 may beconfigured such that the anhedral angle 224 is in the range of fromapproximately 15 to approximately 30 degrees when the wing 50 is underthe approximate 1-g flight loading 78. However, the lower winglet 200may be oriented at any anhedral angle 224, without limitation. The upperwinglet 100 may be oriented at a dihedral angle 124 of at leastapproximately 60 degrees during upward deflection of the wing 50 underthe approximate 1-g flight loading 78. However, the upper winglet 100may be oriented at any dihedral angle 124, without limitation.

Referring to FIGS. 9-10, shown in FIG. 9 is a single upper winglet 280which is provided for comparison only to the winglet system 98 of FIG.10. In this regard, the single upper winglet 280 is not representativeof an embodiment of the winglet system 98 disclosed herein. The singleupper winglet 280 in FIG. 9 is mounted to a wing tip 56 and has awinglet area 290 and center of gravity 284 located at a relatively largelongitudinal offset 286 and relatively large radial offset 288 from thetorsional axis 72 of the wing 50. The single upper winglet 280 in FIG. 9has substantially the same height 282 as the combined height 252 of theupper winglet 100 and the lower winglet 200 in FIG. 10. In addition, thesingle upper winglet 280 in FIG. 9 has the combined winglet area 260 ofthe upper winglet 100 and the lower winglet 200 in FIG. 10 and has aleading edge sweep angle 292 that is substantially equivalent to thesweep angle 114 of the upper winglet 100.

FIG. 10 shows an embodiment of the winglet system 98 as disclosed hereinhaving an upper winglet 100 having a center of gravity 126 and a lowerwinglet 200 having a center of gravity 226. The upper winglet 100 andthe lower winglet 200 have a combined height 252. Advantageously, theupper winglet 100 and the lower winglet 200 have a combined winglet areaand a combined center of gravity 254 that is located at a reducedlongitudinal offset 256 and reduced radial distance 258 from the wingtorsional axis 72 relative to the longitudinal offset 286 of the singleupper winglet 280 of FIG. 9. The upper winglet 100 and lower winglet 200in FIG. 10 are configured such that the longitudinal offset 256 of thecombined center of gravity 254 is less than the longitudinal offset 286of the upper winglet center of gravity 284 of the single upper winglet280 in FIG. 9. Advantageously, the reduced amount of longitudinal offset256 of the combined center of gravity 254 of the presently disclosedwinglet system 98 of FIG. 10 may provide more favorable fluttercharacteristics than the single upper winglet 280 shown in FIG. 9. Forexample, the presently disclosed winglet system 98 of FIG. 10 mayminimize the need for modification or adjustment of the wing 50 that maybe required by the single upper winglet 280 of FIG. 9 such as stiffeningthe wing 50 structure or adding ballast weight (not shown) to the wingleading edge 60 to counteract the inertial effects of the single upperwinglet 280.

FIG. 11 shows an alternative embodiment of the winglet system 98 whereinthe trailing edges 112, 212 of the upper winglet 100 and/or the lowerwinglet 200 are shown generally aligned or coincident with the wingtrailing edge 62. However, the upper winglet 100 and the lower winglet200 may be configured such that the trailing edges 112, 212 of the upperwinglet 100 and/or lower winglet 200 may intersect the wing tip 56 atany location relative to the wing trailing edge 62 and may extend beyondthe wing trailing edge 62 as indicated above. Furthermore, the upperwinglet 100 and lower winglet 200 may be provided with trailing edgefairings (not shown) for transitioning the upper winglet 100 or lowerwinglet 200 into the wing tip 56 and avoid abrupt shape or form changeswhich may result in an increase in drag.

FIG. 12 shows a further embodiment of the winglet system 98 wherein eachone of the upper winglet 100 and the lower winglet 200 includes leadingedge root gloves 138, 238 mounted at the juncture of the upper winglet100 and lower winglet 200 with the wing tip 56. The leading edge gloves138, 238 may be installed at a location proximate the upper and lowerwinglet leading edges 110. 210 of the upper and lower winglets 100, 200.As described above, the leading edge root gloves 138, 238 may provideadditional chord at the upper and lower winglet leading edges 110. 210with minimal increase in area and which may minimize parasitic drag ofthe aircraft 10. The upper winglet 100 and/or the lower winglet 200 maybe configured such that the respective upper winglet root chord 104 andlower winglet root chord 204 have a length that is at leastapproximately 50 percent of the length of the wing tip chord 58. Forexample, the upper winglet 100 and/or the lower winglet 200 may beconfigured such that the respective upper winglet root chord 104 andlower winglet root chord 204 are in the range of from approximately 60to 100 percent or more of the length of the wing tip chord 58.

FIGS. 13-14 illustrate an embodiment of the winglet system 98 whereinthe lower winglet 200 is oriented such that the aerodynamic center ofpressure 230 of the lower winglet 200 is located at a relatively largemoment arm 234 from the intersection of the wing torsional axis 72 withthe wing tip 56. In this regard, the lower winglet 200 is provided witha relatively large leading edge sweep angle 214 (FIG. 5) which resultsin the location of the lower winglet 200 aft of the wing torsional axis72. For example, FIG. 13 illustrates an embodiment of the winglet system98 wherein the lower winglet 200 and the upper winglet 100 are arrangedsuch that an aftmost point 236 of the lower winglet tip 206 is locatedaft of an aftmost point 136 of the upper winglet tip 106.

FIG. 14 illustrates a wind gust 46 acting on the wing 50 and resultingin an increasing lift increment of the lower winglet 200 during the windgust 46. Due to the relatively small anhedral angle 224 (e.g., less than30 degrees—FIG. 8) of the lower winglet 200 when the wing 50 is underthe approximate 1-g flight loading 78, the gust load results in an alower winglet lift increase 232 of the lower winglet 200 which resultsin a nose-down moment 250 on the wing tip 56. The upper winglet 100 mayalso generate an upper winglet lift increase 132 at an upper wingletcenter of pressure 130 due to the gust load. The upper winglet liftincrease 132 may be applied about the relatively short moment arm 134and which may contribute toward the nose-down moment 250 on the wing tip56. However, the magnitude of the upper winglet lift increase 132 may besmall relative to the lower winglet lift increase 232 due to therelatively large dihedral angle 124 (e.g., at least 60 degrees—FIG. 8)of the upper winglet 100 when the wing 50 is under the approximate 1-gflight loading 78.

FIG. 15 is a flow diagram of a method 300 of operating an aircraft 10 orimproving the performance of the aircraft 10 using the winglet system 98disclosed herein.

Step 302 of the method 300 may include providing an upper winglet 100and a lower winglet 200 on a wing 50. As shown in FIG. 7, the lowerwinglet 200 has a static position 240 when the wing 50 is subject to aground static loading 76. As indicated above, the wings 50 may assume agenerally downwardly-deflected shape under the ground static loading 76due to the gravitational force acting on the wings 50 and attachedstructure and systems.

Step 304 of the method 300 may comprise aeroelastically deflecting thewings 50 (FIG. 1) upwardly. For example, the wings 50 may be deflectedupwardly under a steady state, approximate 1-g wing loading duringcruise flight of the aircraft 10. The degree to which the wings 50 aredeflected may be dependent upon the flexibility of the wings 50. In thisregard the sizing and orientation of the upper winglet 100 (FIG. 1) andlower winglet 200 (FIG. 1) may be based in part on the extent ofvertical deflection of the wing tips 56 (FIG. 1) under the approximate1-g wing loading.

Step 306 of the method 300 may comprise moving the lower winglet 200from the static position 240 of the lower winglet 200 to an in-flightposition 242 of the lower winglet 200 during upward deflection of thewing 50 as shown in FIG. 7. The upward deflection of the wing 50 mayalso include aeroelastic upward deflection (not shown) of the lowerwinglet 200 which may increase the effective span of the lower winglet200. The relative span increase 84 or the increase in effective wingspan 80 may also be provided at least in part by movement (e.g.,pivoting) of the lower winglet 200 at the juncture of the lower wingletroot 202 with the wing tip 56.

Step 308 of the method 300 may comprise orienting the lower winglet 200(FIG. 8) at an anhedral angle 224 (FIG. 8) of no less than approximately15 degrees when the wing 50 (FIG. 8) is deflected upwardly under theapproximate 1-g flight loading 78 (FIG. 8). For example, the lowerwinglet 200 may be oriented at an anhedral angle 224 of betweenapproximately 15 degrees and 30 degrees when the wing 50 is under theapproximate 1-g flight loading 78 of the wing. However, the lowerwinglet 200 may be oriented at any anhedral angle 224, withoutlimitation, when the wing 50 is under the approximate 1-g flight loading78.

Step 310 of the method 300 may comprise increasing an effective wingspan 80 of the wing 50 when moving the lower winglet 200 from the staticposition 240 (FIG. 7) to the in-flight position 242 (FIG. 7). Forexample, FIG. 8 illustrates the wing 50 having an effective wing span 80when the wing 50 is under the ground static loading 76. FIG. 8 alsoillustrates the increased effective wing span 82 of the wing 50 when thewing 50 is under the approximate 1-g flight loading 78.

Advantageously, the increase in the effective wing span 80 (FIG. 8) dueto the upward deflection of the wings 50 (FIG. 8) and/or the lowerwinglet 200 (FIG. 8) results in an improvement in the lift-to-dragperformance of the aircraft 10 (FIG. 8) due to the reduction in induceddrag provided by the upper winglet 100 (FIG. 8) and lower winglet 200.

Furthermore, the winglet system 98 advantageously splits or divides thewing tip 56 aerodynamic load of the wing tip 56 between the upperwinglet 100 and the lower winglet 200. Due to the upper and lowerwinglet root chord 104, 204 (FIG. 3) being longer than approximately 50percent of the wing tip chord 58 (FIG. 3), the division or splitting ofthe wing tip 56 aerodynamic load between the upper winglet 100 and thelower winglet 200 reduces the likelihood of flow separation such as whenthe wing 50 is at high angles of attack.

Additionally, the relatively low anhedral angle 224 (FIG. 8) of thelower winglet 200 provides a passive means for exerting a nose-downmoment 250 (FIG. 14) on the wing tip 56 (FIG. 8) during gust loads onthe wing 50 (FIG. 8) with the benefit of minimizing wing bending. Inaddition, as indicated above, a relatively large leading edge sweepangle 214 (FIG. 5) on the lower winglet 200 (FIG. 5) may promote thedevelopment of a steady vortex (not shown) on the lower winglet 200which may reduce flow separation and buffeting at low-speed, high-liftconditions. Even further, by including an upper winglet 100 and a lowerwinglet 200 (FIG. 10) with the winglet system instead of providing asingle upper winglet 280 (FIG. 9), the longitudinal offset 256 (FIG. 10)from the combined center of gravity 254 to the wing torsional axis 72(FIG. 10) provides reduced wing flutter from inertial effects of theupper winglet 100 and lower winglet 200 relative to the wing fluttercaused by larger inertial effects from a longer longitudinal offset of asingle upper winglet 280 (FIG. 9) of equivalent area.

Additional modifications and improvements of the present disclosure maybe apparent to those of ordinary skill in the art. Thus, the particularcombination of parts described and illustrated herein is intended torepresent only certain embodiments of the present disclosure and is notintended to serve as limitations of alternative embodiments or deviceswithin the spirit and scope of the disclosure.

What is claimed is:
 1. A winglet system, comprising: an upper wingletand a lower winglet mounted to a wing; the lower winglet has a length ofapproximately 50-80 percent of a length of the upper winglet; the lowerwinglet having a static position when the wing is subject to anon-ground static loading; and the lower winglet being configured suchthat upward deflection of the wing under an approximate 1-g flightloading causes the lower winglet to move upwardly and outwardly from thestatic position to an in-flight position resulting in an effective spanincrease of the wing under the approximate 1-g flight loading relativeto the span of the wing under the on-ground static loading.
 2. Thewinglet system of claim 1 wherein: the lower winglet is oriented at ananhedral angle of no less than approximately 15 degrees during theupward deflection of the wing under the approximate 1-g flight loading.3. The winglet system of claim 1 wherein: the upper winglet is orientedat a dihedral angle of at least approximately 60 degrees during upwarddeflection of the wing under the approximate 1-g flight loading.
 4. Thewinglet system of claim 1, wherein: an upper winglet tip and a lowerwinglet tip terminate at approximately the same lateral location whenthe wing is under the on-ground static loading.
 5. The winglet system ofclaim 1 wherein: the lower winglet has a center of pressure; the winghaving a wing torsional axis; and the center of pressure of the lowerwinglet being located aft of the wing torsional axis.
 6. The wingletsystem of claim 1, wherein: the wing has a wing tip including a wing tipchord; the upper winglet and the lower winglet each having a root chord;and the upper winglet root chord and the lower winglet root chord eachhaving a length of at least approximately 50 percent of the wing tipchord.
 7. The winglet system of claim 6, wherein: the upper winglet rootchord and the lower winglet root chord each have a length of fromapproximately 60 to 100 percent of a length of the wing tip chord. 8.The winglet system of claim 1, wherein: at least one of the upperwinglet and lower winglet has a leading edge root glove mounted at ajuncture of a wing tip with the respective upper winglet and lowerwinglet.
 9. The winglet system of claim 1, wherein: the upper wingletand the lower winglet each have a taper ratio of tip chord to root chordin a range of from approximately 0.15 to 0.50.
 10. The winglet system ofclaim 1, wherein: the upper winglet and the lower winglet have a leadingedge sweep angle of between approximately 20 and 70 degrees.
 11. Thewinglet system of claim 1, wherein: the wing has a wing torsional axis;the upper winglet and the lower winglet having a combined winglet areaand a combined center of gravity located at a longitudinal offset fromthe wing torsional axis; and the upper winglet and lower winglet beingconfigured such that the longitudinal offset is less than a longitudinaloffset of a center of gravity of a single upper winglet having a wingletarea that is substantially equivalent to the combined winglet area andhaving a leading edge sweep angle that is substantially equivalent tothe upper winglet leading edge sweep angle.
 12. An aircraft, comprising:a pair of wings each having a wing tip; an upper winglet and a lowerwinglet mounted to each one of the wing tips; the lower winglet having astatic position when the wing is subject to an on-ground static loading;the lower winglet having a length of approximately 50-80 percent of alength of the upper winglet; and the lower winglet being sized andoriented such that upward deflection of the wings under an approximate1-g flight loading causes the lower winglet to move upwardly andoutwardly from the static position to an in-flight position resulting inan effective span increase of the wing under the approximate 1-g flightloading relative to the span of the wing under an on-ground staticloading.
 13. A method of enhancing performance of an aircraft,comprising the steps of: providing an upper winglet and a lower wingleton a wing, the lower winglet having a static position when the wing issubject to an on-ground static loading, the lower winglet having alength of approximately 50-80 percent of a length of the upper winglet;upwardly deflecting the wing under an approximate 1-g flight loading;moving the lower winglet upwardly and outwardly from the static positionto an in-flight position during upward deflection of the wing; andcausing an effective span increase of the wing under the approximate 1-gflight loading relative to the span of the wing under the on-groundstatic loading in response to moving the lower winglet upwardly andoutwardly from the static position to the in-flight position.
 14. Themethod of claim 13, further comprising the step of: orienting the lowerwinglet at an anhedral angle of no less than approximately 15 degreesduring the upward deflection of the wing under the approximate 1-gflight loading.
 15. The method of claim 13, further comprising the stepof: orienting the upper winglet at a dihedral angle of at leastapproximately 60 degrees during the upward deflection of the wing underthe approximate 1-g flight loading.
 16. The method of claim 13, wherein:an upper winglet tip and a lower winglet tip terminate at approximatelythe same lateral location when the wing is under the on-ground staticloading.
 17. The method of claim 13, further comprising the steps of:locating the lower winglet such that a center of pressure is aft of awing torsional axis; increasing lift of the lower winglet during a gustload; and exerting a nose-down moment on a wing tip in response to anincrease in the lift of the lower winglet.
 18. The method of claim 17,further comprising the step of: dividing a wing tip aerodynamic loadbetween the upper winglet and the lower winglet, the upper winglet andthe lower winglet each having a root chord having a length of at leastapproximately 50 percent of a wing tip chord.
 19. The method of claim18, further comprising the step of: minimizing parasitic drag of theaircraft by using a leading edge root glove on at least one of the upperwinglet and the lower winglet.
 20. The method of claim 18, furthercomprising the steps of: providing the upper winglet and the lowerwinglet with a combined winglet area and a combined center of gravitythat is longitudinally offset from a wing torsional axis; and reducingwing flutter by longitudinally offsetting the combined center of gravityby an amount that is less than a longitudinal offset of a center ofgravity of a single upper winglet having a winglet area that issubstantially equivalent to the combined winglet area and having aleading edge sweep angle that is substantially equivalent to the upperwinglet leading edge sweep angle.